Which of the following numbers is a factor of 144? ${5,10,11,12,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $144$ by each of our answer choices. $144 \div 5 = 28\text{ R }4$ $144 \div 10 = 14\text{ R }4$ $144 \div 11 = 13\text{ R }1$ $144 \div 12 = 12$ $144 \div 14 = 10\text{ R }4$ The only answer choice that divides into $144$ with no remainder is $12$ $ 12$ $12$ $144$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $144$ $144 = 2\times2\times2\times2\times3\times3 12 = 2\times2\times3$ Therefore the only factor of $144$ out of our choices is $12$. We can say that $144$ is divisible by $12$.